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arXiv · 1411.1391

Double canonical bases

Arkady Berenstein·Jacob Greenstein
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Abstract

We introduce a new class of bases for quantized universal enveloping algebras $U_q(\mathfrak g)$ and other doubles attached to semisimple and Kac-Moody Lie algebras. These bases contain dual canonical bases of upper and lower halves of $U_q(\mathfrak g)$ and are invariant under many symmetries including all Lusztig's symmetries if $\mathfrak g$ is semisimple. It also turns out that a part of a double canonical basis of $U_q(\mathfrak g)$ spans its center.

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Arkady Berenstein, Jacob Greenstein. 2014-11-05. Double canonical bases. https://doi.org/10.1016/j.aim.2017.06.005

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